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Chapter 2: Q 27. (page 237)
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Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
Use the definition of the derivative to prove the following special case of the product rule
State the chain rule for differentiating a composition of two functions expressed
(a) in “prime” notation and
(b) in Leibniz notation.
In Exercises 69–80, determine whether or not f is continuous and/or differentiable at the given value of x. If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.
The total yearly expenditures by public colleges and universities from 1990 to 2000 can be modeled by the function , where expenditures are measured in billions of dollars and time is measured in years since 1990.
(a) Estimate the total yearly expenditures by these colleges and universities in 1995.
(b) Compute the average rate of change in yearly expenditures between 1990 and 2000.
(c) Compute the average rate of change in yearly expenditures between 1995 and 1996.
(d) Estimate the rate at which yearly expenditures of public colleges and universities were increasing in 1995.
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